Radioactive exchange between two surfaces

Percentage Accurate: 86.0% → 96.8%

Time: 5.9s

Precision: binary64

Cost: 1225

• 60.4% of points produce a very large (infinite) output. You may want to add a precondition.

Math

\[{x}^{4} - {y}^{4} \]

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+190} \lor \neg \left(y \leq 4.8 \cdot 10^{+149}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y + x \cdot x\right) \cdot \left(x \cdot x - y \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (pow x 4.0) (pow y 4.0)))

↓

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2e+190) (not (<= y 4.8e+149)))
   (* (* y y) (* y (- y)))
   (* (+ (* y y) (* x x)) (- (* x x) (* y y)))))

C

double code(double x, double y) {
	return pow(x, 4.0) - pow(y, 4.0);
}

↓

double code(double x, double y) {
	double tmp;
	if ((y <= -2e+190) || !(y <= 4.8e+149)) {
		tmp = (y * y) * (y * -y);
	} else {
		tmp = ((y * y) + (x * x)) * ((x * x) - (y * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x ** 4.0d0) - (y ** 4.0d0)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2d+190)) .or. (.not. (y <= 4.8d+149))) then
        tmp = (y * y) * (y * -y)
    else
        tmp = ((y * y) + (x * x)) * ((x * x) - (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	return Math.pow(x, 4.0) - Math.pow(y, 4.0);
}

↓

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2e+190) || !(y <= 4.8e+149)) {
		tmp = (y * y) * (y * -y);
	} else {
		tmp = ((y * y) + (x * x)) * ((x * x) - (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	return math.pow(x, 4.0) - math.pow(y, 4.0)

↓

def code(x, y):
	tmp = 0
	if (y <= -2e+190) or not (y <= 4.8e+149):
		tmp = (y * y) * (y * -y)
	else:
		tmp = ((y * y) + (x * x)) * ((x * x) - (y * y))
	return tmp

Julia

function code(x, y)
	return Float64((x ^ 4.0) - (y ^ 4.0))
end

↓

function code(x, y)
	tmp = 0.0
	if ((y <= -2e+190) || !(y <= 4.8e+149))
		tmp = Float64(Float64(y * y) * Float64(y * Float64(-y)));
	else
		tmp = Float64(Float64(Float64(y * y) + Float64(x * x)) * Float64(Float64(x * x) - Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp = code(x, y)
	tmp = (x ^ 4.0) - (y ^ 4.0);
end

↓

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2e+190) || ~((y <= 4.8e+149)))
		tmp = (y * y) * (y * -y);
	else
		tmp = ((y * y) + (x * x)) * ((x * x) - (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := If[Or[LessEqual[y, -2e+190], N[Not[LessEqual[y, 4.8e+149]], $MachinePrecision]], N[(N[(y * y), $MachinePrecision] * N[(y * (-y)), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * y), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision] * N[(N[(x * x), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0000000000000001e190 or 4.80000000000000024e149 < y

   1. Initial program 65.4%

      \[{x}^{4} - {y}^{4} \]

   2. Applied egg-rr 75.0%

      \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]
      Step-by-step derivation

      [Start] 65.4%	\[ {x}^{4} - {y}^{4} \]
      sqr-pow [=>] 65.4%	\[ \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]
      sqr-pow [=>] 65.4%	\[ {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]
      difference-of-squares [=>] 75.0%	\[ \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]
      metadata-eval [=>] 75.0%	\[ \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      pow2 [<=] 75.0%	\[ \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      metadata-eval [=>] 75.0%	\[ \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      pow2 [<=] 75.0%	\[ \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      metadata-eval [=>] 75.0%	\[ \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      pow2 [<=] 75.0%	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      metadata-eval [=>] 75.0%	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]
      pow2 [<=] 75.0%	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

   3. Taylor expanded in x around 0 75.0%

      \[\leadsto \color{blue}{{y}^{2}} \cdot \left(x \cdot x - y \cdot y\right) \]

   4. Simplified 75.0%

      \[\leadsto \color{blue}{\left(y \cdot y\right)} \cdot \left(x \cdot x - y \cdot y\right) \]
      Step-by-step derivation

      [Start] 75.0%	\[ {y}^{2} \cdot \left(x \cdot x - y \cdot y\right) \]
      unpow2 [=>] 75.0%	\[ \color{blue}{\left(y \cdot y\right)} \cdot \left(x \cdot x - y \cdot y\right) \]

   5. Taylor expanded in x around 0 90.4%

      \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\left(-1 \cdot {y}^{2}\right)} \]

   6. Simplified 90.4%

      \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(-y\right)\right)} \]
      Step-by-step derivation

      [Start] 90.4%	\[ \left(y \cdot y\right) \cdot \left(-1 \cdot {y}^{2}\right) \]
      unpow2 [=>] 90.4%	\[ \left(y \cdot y\right) \cdot \left(-1 \cdot \color{blue}{\left(y \cdot y\right)}\right) \]
      mul-1-neg [=>] 90.4%	\[ \left(y \cdot y\right) \cdot \color{blue}{\left(-y \cdot y\right)} \]
      distribute-rgt-neg-out [<=] 90.4%	\[ \left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(-y\right)\right)} \]

   if -2.0000000000000001e190 < y < 4.80000000000000024e149

   1. Initial program 91.7%

      \[{x}^{4} - {y}^{4} \]

   2. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]
      Step-by-step derivation

      [Start] 91.7%	\[ {x}^{4} - {y}^{4} \]
      sqr-pow [=>] 91.5%	\[ \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]
      sqr-pow [=>] 91.4%	\[ {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]
      difference-of-squares [=>] 99.7%	\[ \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]
      metadata-eval [=>] 99.7%	\[ \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      pow2 [<=] 99.7%	\[ \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      metadata-eval [=>] 99.7%	\[ \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      pow2 [<=] 99.7%	\[ \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      metadata-eval [=>] 99.7%	\[ \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      pow2 [<=] 99.7%	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]
      metadata-eval [=>] 99.7%	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]
      pow2 [<=] 99.7%	\[ \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+190} \lor \neg \left(y \leq 4.8 \cdot 10^{+149}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y + x \cdot x\right) \cdot \left(x \cdot x - y \cdot y\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	96.8%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+190} \lor \neg \left(y \leq 4.8 \cdot 10^{+149}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y + x \cdot x\right) \cdot \left(x \cdot x - y \cdot y\right)\\ \end{array} \]

Alternative 2
Accuracy	90.8%
Cost	1232

\[\begin{array}{l} t_0 := \left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right)\right)\\ t_1 := \left(y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+187}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-74}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot y + x \cdot x\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	71.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+185} \lor \neg \left(y \leq 4.8 \cdot 10^{+149}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)\\ \end{array} \]

Alternative 4
Accuracy	66.2%
Cost	777

\[\begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+251} \lor \neg \left(x \leq 2.4 \cdot 10^{+111}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	32.4%
Cost	448

\[\left(y \cdot y\right) \cdot \left(x \cdot x\right) \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))